All the older Jags run with 4HA. The ones with the LSD fitted have a larger bulge in the diff cover, also the easy test to see if it's an LSD is to turn one hub and the other should rotate the same way.
My axle is from an XK120 and is fitted with an XJ6 crown wheel and pinion. Some of the "screemer" ratios available need spacers fitting in the diff but I would expect them to be in the diff you are stripping 

Edited 1 time by OCX440X Aug 5 11 6:37 AM.